This invention relates to a method for computing a progressive spectacle lens, and also to a method for manufacturing a spectacle lens of this kind, drop plate kind molds, casting molds for casting, or molding plugs for press-forming spectacle lenses of this kind from a plastics material.
Progressive spectacle lenses (also called varifocal lenses, multifocal lenses etc.) are usually understood to be spectacle lenses having a different (smaller) power in the region through which a spectacles wearer views an object located at a great distancexe2x80x94hereunder designated as a distance portionxe2x80x94than in the region (near portion) through which the spectacles wearer views a near object. Located between the distance portion and the near portion is the so-called progressive zone in which the power of the spectacle lens continuously increases from that of the distance portion to that of the near portion. The magnitude of the power increase is also designated as addition power.
As a rule, the distance portion is located in the upper part of the spectacle lens and designed for viewing xe2x80x9cto infinityxe2x80x9d, whilst the near portion is located in the lower region and is particularly designed for reading. In spectacles for special applicationsxe2x80x94those for pilots or for monitor work stations are mentioned as examplesxe2x80x94the distance and near portions may also be arranged differently and/or designed for other distances. Furthermore, it is possible for a plurality of near portions and/or distance portions and suitable progressive zones to be present.
With progressive spectacle lenses having a constant refractive index it is necessary, for the power to increase between the distance portion and the near portion, that the curvature of one or both surfaces continuously change from the distance portion to the near portion.
The surfaces of spectacle lenses are usually characterized by the so-called principal radii of curvature R1 and R2 at every point on the surface. (Sometimes also the principal curvatures K1=1/R1 and K2=1/R2 are given instead of the principal radii of curvature.) Together with the refractive index of the glass material, the principal radii of curvature govern the parameters frequently used for an ophthalmologic characterization of a surface:
Surface power=0.5xc2x7(nxe2x88x921)xc2x7(1/R1+1/R2)
Surface astigmatism=(nxe2x88x921)xc2x7(1/R1xe2x88x921/R2).
Surface power is the parameter via which an increase of power from the distance portion to the near portion is achieved. Surface astigmatism (more clearly termed cylinder power) is a xe2x80x9ctroublesome propertyxe2x80x9d, because an astigmatismxe2x80x94inasmuch as an eye does not have an innate astigmatism to be correctedxe2x80x94which exceeds a value of about 0.5 dpt results in an indistinctly seen image on the retina.
Although any change of the curvature of the surface which is needed to achieve a surface power increase without vision being xe2x80x9cdisturbedxe2x80x9d by surface astigmatism can be attained relatively simply along a (plane or curved) line, considerable xe2x80x9cintersectionsxe2x80x9d of surfaces will result alongside this line, leading to a large surface astigmatism which more or less impairs the lens in regions alongside the mentioned line. According to Minkwitz"" Law, for a line lying in a plane and designed as a umbilical line, the surface astigmatism in the direction perpendicular to the umbilical line increases with a gradient which is twice that of the surface power along the umbilical line, so that, particularly in the progressive zone, disturbing values of the surface astigmatism already result close to the umbilical line. (A line which at every point has the same principal curvatures, i.e. is free of surface astigmatism, is termed a navel line or umbilical lime or ombilical line).
For this reason, the designing of a progressive spectacle lens surface contributing to power change has in the past started out from a line lying in a plane or extending in a sinuous mannerxe2x80x94also termed a principal meridian or a principal linexe2x80x94which runs centrally along the surface from top to bottom, and approximately follows the principal viewing line. A principal viewing line is understood to be a series of points of penetration of the rays of sight directed through the spectacle lens surface onto objects located at different distances centrally in front of the nose during a movement, in particular a lowering, of the glance. The principal curvatures of each point of this line were chosen in such manner that the desired increase of the surface power from the distance portion to the near portion is achieved. Setting out from this line, (more or less) suitable computations were then made of the lateral regions of the surface using various methods or approaches.
In case of a planar principal line (i.e. principal meridian), the spectacle lens, when being fitted into a spectacle frame, is usually tilted by about 8xc2x0 to 10xc2x0, so that the principal meridian extends obliquely from top to bottom in correspondence with the convergence of the eyes. Progressive spectacle lenses having a planar principal meridian are described, for example in U.S. Pat. No. 2,878,721 or DE-AS 20 44 639.
Attention is expressly drawn to these publicationsxe2x80x94as well as to all publications mentioned in the followingxe2x80x94concerning all remaining terms not described here in greater detail.
Because the principal viewing line on a spectacle lens surface is not a straight or planar line, the use of a planar principal meridian always represents a compromise. For this reason it has been suggested for a long time that a sinuous linexe2x80x94also designated as a principal linexe2x80x94be used as a xe2x80x9cconstruction backbonexe2x80x9d for a progressive surface, the course of which follows, as well as possible, the actual course of the principal viewing line as determined by physiology, and not by the structure (!) of the spectacle lens.
Progressive spectacle lenses having a sinuous principal line have been described in many patent publications.
Attention drawn to U.S. Pat. No. 4,606,622 only as an example. In this publication, however, no details can be found of how the course of the principal line can be made xe2x80x9cto coincidexe2x80x9d with the principal viewing line.
Although various other publications are concerned with the course of the principal line, the approaches made therein are unsatisfactoryxe2x80x94as will be set out in the following:
For the surfaces described in DE-C-42 38 067 and DE-C-43 42 234 the course of the principal line is composed of straight sections; in this, the angles between the straight lines vary in dependence on the addition power. To compose the principal line from straight sections is an unsuitable approach, because the principal line must be twice differentiable. To vary the principal line in dependence only on the addition power, in order to bring it into coincidence with the principal viewing line, is also unsatisfactory, because the principal viewing line depends on many other parameters. Furthermore, in these publications no method is given of how a progressive surface may be designed around this principal line to have properties as specified along the principal line.
The European Patent Application 88 307 917 describes that the course of the principal line should be varied in dependence onxe2x80x94and only onxe2x80x94the addition power. Apart from this, the course of the principal line is stipulated, presumably in the expectation that it will coincide with the principal viewing line.
In DE-A-196 12 284, in which the distinction made in the present application between principal line (construction line of at least one surface of the spectacle lens) and principal viewing line (physiological property) is not made, and which instead mentions only a principal viewing line (which, after all, is a property of the spectacle lens), a spectacle lens is described having a principal linexe2x80x94or more precisely stated, an offset principal linexe2x80x94which varies in dependence on the power of the distance portion (stronger principal meridian) and the addition power. Whether a principal line of this kind coincides with the actual principal viewing line is not investigated more closely. Furthermore, no method is given for determining the principal viewing line. Similarly, it is not taken into consideration that the principal viewing line depends on many other parameters, and that if the principal line is varied only in dependence on the addition power and the distance portion power, then it cannot coincide with the actual principal viewing line.
In the patent application PCT/DE95/00438 a principal line is described, the course of which has the form             x      0        ⁢          (      y      )        =      b    +    a    -          a              1        +                  ⅇ                      c            ⁢                          (                              y                +                d                            )                                          
How this principal line may be conformed to the principal viewing line is not described in detail.
In accordance with the invention it has been realized that in many cases, for example with an astigmatic prescription including an oblique cylinder axis, this form is not satisfactory for bringing the principal line into coincidence with the principal viewing line.
In DE-A-43 37 369 a method is described for computing a strip of second order. A method for computing a strip of second order which coincides with the principal viewing line is not given.
The invention is based on the object of providing a method for computing a progressive spectacle lens in which certain properties of power and astigmatism are present along a linexe2x80x94referred to as a principal line in the followingxe2x80x94and in which this line coincides with the principal viewing line. Moreover, a suitable method of manufacture is to be described.
An achievement of this object in accordance with the invention is described in patent claim 1. Further developments of the invention are the subject matter of claims 2 to 18. In claims 19 and 20 methods for manufacturing appropriate surfaces or spectacle lenses are given.
The invention is based on the fundamental concept of departing from the hitherto usual practice of stipulating a principal linexe2x80x94possibly in dependence on certain parametersxe2x80x94as an unchangeable construction-backbone of the progressive surface for optimizing the surface, and instead of this, proceeding in an opposite manner, i.e. by first determining the principal viewing line on a surface computed by means of a first approximation, and then conforming the course of the principal line, and with it the surface, to the actual course of the principal viewing line. Only by proceeding in this manner in accordance with the invention is it possible to bring these two lines into coincidence.
The method according to the invention is rendered distinct, in particular, by the following steps:
a. stipulating as initial parameters a course of a projection x0(y) of the principal line on the x,y plane, and also properties of the spectacle lens along the principal line whilst taking into account spherical, cylindrical, and possibly also prismatic prescription values and the addition power, as well as an interpupillary distance, and computing from these stipulations at least one strip of second order on a progressive surface of the spectacle lens;
b. stipulating an object-distance function Al(y) which describes a change of object distance with a movement, in particular a lowering, of a glance;
c. determining on each horizontal meridian of the progressive spectacle lens a point of penetration of a principal ray through the progressive surface, for which point a distance of a point of intersection of this principal ray with a plane which bisects the interpupillary distance is equal to the object distance given by the object-distance function Al(y);
d. computing for the entirety of these points of penetration lying on the principal viewing line a course of the projection xxe2x80x20(y) on the x,y plane;
e. equating the course x0(y) to xxe2x80x20(y) and checking the coincidence;
f. subsequently iteratively repeating the steps a. to e. until the projection x0(y) of the principal line is equal (within given limits) to the course of the principal viewing line projection xxe2x80x20(y) used for the computation of the respective surface.
The principal line as a sinuous line is unequivocally defined by two projections, for example the projection x0(y) on the x,y plane and the projection z0(y) on the y,z plane.
For computing a spectacle lens or the respective progressive surface based on a principal line coinciding at least within given limits with the principal viewing line, a course of the projection x0(y) of the principal line, based for example on values of experience, is first stipulated, and then, using this projection and the other stipulations of properties along the principal line, a spectacle lens is designed in the form of at least a strip of second order.
Next, the points of penetration of the principal rays through the progressive spectacle lens, i.e. the rays passing through the center of rotation of the eye, are computed. On each horizontal meridian the point of penetration through the progressive surface is selected, at which the distance from the point of penetration through the front surface to the point of intersection of the principal ray with the central plane, that is the vertical plane which bisects the interpupillary distance, corresponds to the stipulated object distance Al(y). The object distance function Al(y) may be determined, for example empirically or by measurement, for a particular spectacles wearer.
The thus determined points of penetration through the progressive surface form the principal viewing line. Now the projection x0(y) of the principal line is equated to the principal viewing line, i.e. the spectacle lens is designed a second time, and the principal viewing line is computed once again. This is repeated until the principal line and the principal viewing line coincide. As a rule, one iteration step will already be sufficient.
The properties stipulated for the computation of the spectacle lens may be, for example, surface properties and in particular the surface astigmatism A0(y) and the mean surface power D0(y) on the principal line, wherein the vertex height z and the derivatives xcex4z/xcex4x and xcex4z/xcex4y at one point on the principal line are stipulated as initial conditions.
A progressive spectacle lens of this kind can be described with a sinuous principal line and any horizontal meridian, e.g. with a power series.
Each horizontal meridian may then be described by       z    ⁢          (              x        ,                  y          c                    )        =                    x        0            ⁢              (                  y          c                )              +                  z        0            ⁢              (                  y          c                )              +                  ∑                  i          =          1                n            ⁢                        a          i                ·                              (                          x              -                                                x                  0                                ⁢                                  (                                      y                    c                                    )                                                      )                    i                    
or the entire surface may be described by       z    ⁢          (              x        ,        y            )        =                    x        0            ⁢              (        y        )              +                  z        0            ⁢              (        y        )              +                  ∑                  i          =          1                n            ⁢                                    a            i                    ⁢                      (            y            )                          ·                                            (                              x                -                                                      x                    0                                    ⁢                                      (                    y                    )                                                              )                        i                    .                    
By stipulating the projection of the principal line and a particular surface astigmatism and a particular mean surface power on the principal line, as well as the initial conditionsxe2x80x94vertex height z and the two derivatives             ∂      z              ∂      x        ⁢      xe2x80x83    ⁢  and  ⁢      xe2x80x83    ⁢            ∂      z              ∂      y      
at a particular position, a so-called strip of second order is unequivocally determined. This precisely leads to
a projection z0(y) and
a respective course of the coefficients a1(y) and a2(y).
These parameters may be computed either by solving the system of differential equations or with the aid of a target function. The higher order coefficients a3(y) to An(y) (hence the term xe2x80x9cstrip of second orderxe2x80x9d) may be chosen freely and may be used for optimizing the periphery of the spectacle lens.
Of course, any other surface representation which can be differentiated (at least) twice is possible.
In this, the stipulated surface astigmatism A0(y) is determined by its magnitude and its cylinder axis. The deviation from the stipulated astigmatism A0(y) is computed, for example, by means of the cross-cylinder method which takes account of the magnitude and also the cylinder axis.
Cross-cylinder method:
cylx=cylactxc2x7cos(2xc2x7Aact)xe2x88x92cyldes cos(2xc2x7Ades)
cyly=cylactxc2x7sin(2xc2x7Aact)xe2x88x92cyldesxc2x7sin(2xc2x7Ades)
cylres=√{square root over (cylx2+cyly2)}
      A    res    =      a    ⁢          xe2x80x83        ⁢          tan      ⁢              (                              cyl            y                                cyl            x                          )            
wherein:
cylact,Aact actual cylinder (spectacle lens): magnitude and cylinder axis
cyldes,Ades desired cylinder (prescription): magnitude and cylinder axis
cylres,Ares resulting cylinder (astigmatic error): magnitude and cylinder axis
If, for example, the prescription reads:
Cylinder: 2.5 dpt, axis: 0 degrees according to TABO, and the computed spectacle lens has at one point on the principal line a cylinder power of 2.5 dpt and a cylinder axis of 2 degrees, then the astigmatic error obtained is
0.174 dpt.
However, in accordance with the invention it is preferred that the properties of the spectacle lens in a wearing position be stipulated, and not the surface properties. In particular, these properties may be the astigmatism and the power of the combination xe2x80x9cspectacle lens/eyexe2x80x9d.
For computing a progressive surface in the wearing position, a wearing situation is stipulated. This relates either to a definite user for whom the individual parameters in the respective wearing position are especially determined and the progressive surface is separately computed, or to average values, as described for example in DIN 58 208, Part 2.
As an initial condition the thickness of the spectacle lens is stipulated instead of the vertex height z, and the prismatic power at a definite position is stipulated instead of the two differentials. Additionally needed are a surface description of the second surface which in particular may be a spherical or an aspherical surface, and the refractive index of the spectacle lens, the interpupillary distance and the distance of the center of rotation of the eye, the pantoscopic angle and the lateral inclination of the spectacle lens, and the object-distance function Al(y).
The values may be standardized or average values of a wearing position, or even better, individually determined data of the prospective spectacles wearer. In this, the actual spectacle frame and its arrangement in front of the eye of the future spectacles wearer may be taken into account in determining the data.
It is the aim of the first part of the computation for the projection x0(y) of the principal line on the x,y plane to coincide with the projection of the principal viewing line on the x,y plane. Only thereby can it be achieved that the spectacles wearer may have the predetermined (and thus optimum) properties along the principal viewing line, where the main problems of viewing arise.
Because the principal viewing line also depends on the prismatic power in each horizontal meridian, the coincidence may be achieved only by iterationxe2x80x94as has already been stated.
After the iteration problem has been solved, a spectacle lens is obtained for which the imaging properties along the principal viewing line correspond exactly to the stipulated values. For this, all of the individual parameters such as interpupillary distance, distance of center of rotation of the eye, spherical, cylindrical and prismatic prescription values, addition power, object distance, pantoscopic angle and lateral inclination of the spectacles, thickness, refractive index and base curve of the spectacle lens are taken into account during the determination of the principal viewing line.
The functions which describe the course of the projection and the given properties, such as the surface astigmatism or (residual) astigmatism of the system eye/spectacle lens, and also the surface power or the power, must be continuously differentiable (at least) twice and flexible enough to reproduce the stipulated properties.
Suitable functions for the projection x0(y) of the principal line and also the stipulated properties are, for example, cubic or higher-order spline functions or a function f(y) of the form       f    ⁡          (      y      )        =      b    +    a    -          a                        (                      1            +                          ⅇ                              c                ⁡                                  (                                      y                    +                    d                                    )                                                              )                m              +                  ∑        i            ⁢                        g          i                ⁢                              y            i                    .                    
Furthermore, it is not only possible, starting out from the strip of second order for which the principal line coincides (at least within given limits) with the principal viewing line, and on which the stipulated properties are attained, to compute the individual horizontal meridians (y=yc) by means of the following function       z    ⁢          (              x        ,                  y          c                    )        =                    x        0            ⁢              (                  y          c                )              +                  z        0            ⁢              (                  y          c                )              +                  ∑                  i          =          1                n            ⁢                        a          i                ·                              (                          x              -                                                x                  0                                ⁢                                  (                                      y                    c                                    )                                                      )                    i                    
but alsoxe2x80x94once again starting out from the strip of second order on which the principal line coincides (at least within given limits) with the principal viewing linexe2x80x94to compute the entire surface by means of cubic or higher order spline functions and usual optimizing methods.
The method of the invention may be employed for any desired surfaces, such as those of spectacle lenses in which the progressive surface is the front surface and which are fabricated as blanks having certain gradations (base curve system).
However, it is particularly preferred to employ the method of the invention with spectacle lenses for which the progressive surface is the eye-side surface and is computed individually for a particular spectacles wearer. For this, the front surface may be a spherical or aspherical surface and, in particular, a toroidal or atoroidal surface, wherein the cylinder power imparted by the toroidal or atoroidal surface does not necessarily have to serve to compensate an astigmatism of the respective eye. The toroidicity may also be chosen for reasons of appearance, as was described in an earlier application.
For this, the progressive surface computed in accordance with the invention may also serve in a manner known per se in the manufacture of a progressive spectacle lens by means of any surface-shaping or surface-working method.
For example, the surface data may be employed directly to control a grinding machine and possibly also to control a polishing operation of a spectacle lens blank of any desired silicate glass or a plastics material (having any refractive index). Suitable numerically controlled grinding and polishing machines are generally known.
Of course, the surface data may also be used for manufacturing casting molds for the casting, and drop plate type molds or molding plugs for the press-forming of spectacle lenses from a plastics material.
For this it is possible to add xe2x80x9ccorrection dataxe2x80x9d to the determined surface data, which take into account errors during the manufacturing operation in a known manner. Errors of the prefabricated second surface, which have been determined in particular by measurement technology, may also be taken into account in the compulation of the progressive surface.
The data may be used in the same way for the second surface and the arrangement of the two surfaces relative to each other in the manufacture of the spectacle lens by working the second surface, or in arranging the second casting mold relative to the casting mold for the progressive surface.